According to resummed perturbation theory, certain scalar theories have a global symmetry, which is restored in the vacuum but is broken at high temperatures. Recently, this phenomenon has been studied with 4d finite temperature lattice simulations, and it has been suggested that the non-perturbative dynamics thus incorporated would hinder the transition. We have carried out another lattice study, for a theory with very small coupling constants. We find perfect compatibility with next-to-leading order resummed perturbation theory, and demonstrate that "inverse" symmetry breaking can indeed take place at high temperatures. (C) 1998 Elsevier Science B.V. All rights reserved.